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Solutions and Activities to

CHAPTER

5

EXTERNALITIES: PROBLEMS AND SOLUTIONS

Questions and Problems 1. Peterson, Hoffer, and Millner (1995) showed that air bag use has led to increases in car crashes. Despite this finding, the government mandates that new cars have air bags, rather than taxing their use. Is this policy a contradiction?

There are a number of rationales for a policy that requires air bags even though they are associated (causally?) with more car crashes. First, perhaps injuries among passengers protected by air bags are fewer or less severe than they would be without air bags, even if crashes are more frequent. Second, passive restraint systems such as air bags protect people who are unable or unwilling to protect themselves by using seat belts. Given either of these rationales, the use of air bags might reduce the costs of being in an accident, which would lower insurance premiums for all of us. The correlation between air bag installation and car crashes may not be causal. If other conditions changed at the same time that air bag use increased, then air bags may not have caused the increase in crashes. For example, speed limits have been raised in some areas which may have contributed to the increase in car crashes. Population growth and the expansion of urban and suburban areas may also have contributed to the rise in crashes by increasing highway congestion. An alternative explanation for an observed relationship between air bag use and car crashes is “moral hazard.” Moral hazard occurs when people increase their risk-taking behavior (or other behaviors) when new policies make that behavior less costly. In this case, drivers may take more driving risks knowing that they will be protected by their air bags in the event of an accident. 2. When the state of Virginia imposed stricter regulations on air pollution in 2003, it also authorized an auction of pollution permits, allowing some plants to emit larger amounts of ozone-depleting chemicals than would otherwise be allowed, and some to emit less. Theory predicts that this auction will lead to a socially efficient allocation of pollution. Describe how this outcome would occur.

The use of auctions to reduce pollution exploits differences among firms: each firm gets to choose its own least-cost way of operating. Firms that can reduce emissions relatively cheaply will be able to profit by reducing their emissions and then selling unneeded permits to firms for which emissions reduction is more costly. The difference in costs means there is room for mutually beneficial trades. For example, firm A may be able to reduce emissions by 1 ton for $100; firm B may be able to reduce emissions by 1 ton for $150. If firm A cuts its emissions by an extra ton and then sells its unneeded permit for $125 to firm B, both firms have a net gain of $25. As in any market, self-interested firms will trade until all mutually beneficial trades have taken place, a socially efficient outcome. In this case, pollutionreduction steps are taken by the firms that can do so at the lowest cost.

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Jonathan Gruber / Finance and Public Policy

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3. Can an activity generate both positive and negative externalities at the same time? Explain your answer.

Sometimes externalities are in the eye (or nose, or ear) of the beholder. If you like the music your roommate plays, you can free ride when he or she is playing music, enjoying a positive externality. Your other roommate, though, who hates that kind of music, would experience a negative externality. Sometimes a positive externality becomes too much of a good thing. During the holiday season, some people construct elaborate displays that everyone can enjoy just by driving by them. But if too many people drive by every night, traffic congestion becomes a problem for those living in the neighborhood: for them, the holiday display creates a negative externality. 4. In the midwestern United States, where winds tend to blow from west to east, states tend to more easily approve new polluting industries near their eastern borders than in other parts of the state. Why do you think this is true?

A cynical explanation would be that states can export air pollution by locating their dirtiest plants near their eastern borders, allowing the pollutants to blow into neighboring states. However, two tendencies that yield a correlation (winds tend to blow . . . and states tend to approve . . .) are not necessarily causally related. There may be another explanation. Possibly because of patterns of settlement (east to west), large cities in midwestern states tend to be located on the eastern borders of their states; examples include Detroit, Chicago, Milwaukee, and the Twin Cities. It may be that industrial plants tend to be located near such population (employment) centers. 5. Can government assignment and enforcement of property rights internalize an externality? Will this approach work as well as, better than, or worse than direct government intervention? Explain your answers and describe one of the difficulties associated with this solution.

The Coasian approach of assigning property rights and then allowing the affected parties to negotiate a solution can internalize an externality. If one party has a clear, enforceable right to curtail an activity that generates an externality, then the injured party or parties have an incentive to pay the externality generator to stop or curtail that activity. Similarly, if the injured parties have a right to be free of an externality but also have an enforceable right to sell that freedom, a person or firm who profits from generating that externality might be able to negotiate for the purchase of the right to operate. This might be better than government intervention when the number of affected people is small and there are no barriers to negotiation. Social norms or large power or wealth differentials, however, could deter negotiation. For example, a manufacturing firm might easily pay off residents of a poor neighborhood to acquire the right to dispose of toxic materials, which some people might regard as inequitable. Some other difficulties with this solution arise when there are too many affected parties to be able to negotiate a transaction; when one of the affected parties engages in the “holdout” strategy; and when it is difficult to identify the source of the externality. 6. In close congressional votes, many members of Congress choose to remain “undecided” until the last moment. Why might they do this? What lesson does this example teach about a potential shortcoming of the Coasian solution to the externality problem?

Members of Congress who remain undecided until the last moment may be engaging in a form of the holdout strategy. Suppose vote trading, or logrolling, is occurring with respect to a piece of legislation. The sponsor of the bill might offer his or her support for other bills in exchange for votes on this bill. As the call for the vote approaches, the sponsor may be willing to offer more in order to obtain the support needed to pass the bill, so remaining un-

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Jonathan Gruber / Finance and Public Policy

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decided increases a Congress member’s negotiating strength. The situation in which legislators fail to commit their votes until the final hour is analogous to the holdout problem that exists with Coasian solutions that involve several parties. If the purchaser of the right to impose an externality needs to strike a deal with many sellers, each individual seller can delay settling in order to pressure the purchaser to increase the price. 7. Suppose that the marginal private cost of production of a good is MC = 10 + 2Q and the marginal external cost associated with that good’s production is $10 per unit. What is the marginal private cost associated with the tenth unit produced? What is the marginal social cost associated with the tenth unit?

When quantity is 10, marginal private cost is 10 + 2(10) = 10 + 20 = 30. Marginal social cost = marginal private cost + marginal external cost. The marginal external cost is 10, so marginal social cost is 40. 8. Explain why the private marginal cost (or benefit) diverges from the social marginal cost (or benefit) in the case of an externality.

Private marginal costs and benefits are actual costs incurred and benefits enjoyed by a person, firm, or other entity. These are the implicit and explicit costs and benefits that economists assume are taken into account when someone is making an optimal choice. An externality is, by definition, a cost or benefit that is experienced by a person, firm, or other entity who is not part of the original transaction. For example, a cigarette seller must consider production and distribution costs and a cigarette buyer must consider utility when making a transaction. In the absence of regulation, liability, or social norms, neither has an incentive to consider the effects of secondhand smoke: that cost falls on a person who is not part of the original transaction. That external cost is a real cost associated with the act of smoking, but it is not included in the calculations of the buyer and seller. From a societal point of view, resources are not optimally allocated when some costs or benefits are ignored. 9. Why do governments sometimes impose quantity regulations that limit the level of negative-externality-inducing consumption? Why do governments sometimes impose price regulations by taxing this consumption?

For some kinds of externalities, the goal of policy is to limit the quantity of the externality. This is likely to be true when we know fairly precisely the harm associated with levels of exposure to the externality and when that harm increases fairly steeply with increased levels of exposure. In these cases, it is a priority to limit the amount of the negative externality, even though the cost of the restriction might be fairly high. For other kinds of externalities, the marginal harm imposed may not be as well known or may not increase substantially with small increases in exposure. In these cases, where the amount of the marginal exposure to the externality is not as critical, policy makers will seek to limit the externality by taxing consumption. The elasticity of demand for the externality-generating commodity also matters in the decision to tax. If demand is inelastic, taxing it will raise government revenues but won’t reduce consumption by a proportional amount. On the other hand, if demand is elastic, taxing the commodity will reduce its consumption but will raise proportionally less tax revenue. There may also be a political component to these differences. Taxing consumption of a good that generates a negative externality—gasoline, for example—implies that wealthier individuals can purchase the right to generate the externality. Quantity restrictions may seem more equitable but may also be seen as violations of our freedoms.

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Jonathan Gruber / Finance and Public Policy

10. Answer the following two questions for each of the following examples: (i) smoking by individuals; (ii) toxic waste production by firms; (iii) research and development by a high-tech firm; and (iv) individual vaccination against communicable illness. a. Is there an externality? If so, describe it, including references to whether itis positive or negative, and whether it is a consumption or production externality.

i. Smoking by individuals generates negative consumption externalities by generating secondhand smoke. ii. Toxic waste production by firms generates negative production externalities because the harm (or toxicity) is a by-product of the firm’s production. iii. Research and development by a high-tech firm generates positive production externalities when the results of that research expand the knowledge and productivity of all firms. iv. Individual vaccinations generate positive consumption externalities by reducing the number of people in the population who have a communicable illness. When the number of infected people is reduced, the probability of catching the illness is reduced for everyone. b. If there is an externality, does it seem likely that private markets will arise that allow this externality to be internalized? Why or why not?

i. The problem of secondhand smoke is unlikely to be solved by private markets. Smoke is widely dispersed, making it difficult to account for and negotiate with every affected person. In addition, the value of smoking a single cigarette is likely to be small relative to the transaction costs of negotiating the solution. ii. The problem of toxic waste might be amenable to a private market solution. The generator can be easily identified, and a finite number of people are affected. If the number of affected people is relatively small and the firm places a high dollar value on its ability to dispose of the material, there may be room for a mutually beneficial trade, even when transaction costs are considered. This is even more likely to be true in a poorer neighborhood. iii. A firm that purchases a patent or license is in some sense using a market mechanism to partially compensate the researching firm for its contribution to the knowledge base. However, it is hard to completely restrict or contain the flow of information. It is unlikely that a private market for intellectual property could completely internalize this externality. iv. Private compensation for the reduced risk of exposure associated with vaccinations seems unlikely. It would be virtually impossible to identify the beneficiaries of increased vaccination rates.

Advanced Questions 11. Warrenia has two regions. In Oliviland, the marginal benefit associated with pollution cleanup is MB = 300 – 10Q, while in Linneland, the marginal benefit associated with pollution cleanup is MB

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Oliviland is equal to 28.8. For Linneland, the marginal benefit is 200 – 4Q. Setting that equal to 12 yields 200 – 4Q = 12, or 188 = 4Q. The optimal level in Linneland is equal to 47. 12. The private marginal benefit associated with a product’s consumption is PMB = 240 – 2P and the private marginal cost associated with its production is PMC = 4P. Furthermore, the marginal external damage associated with this good’s production is MD = 2P. What level of taxation would generate the socially efficient level of the good?

The goal of the tax is to internalize the externality by equating private marginal cost with social marginal cost. A tax in the amount of the external damage forces the firm to consider that cost in determining its output. A tax equal to 2P will achieve social efficiency. 13. Suppose that demand for a product is Q = 1,200 – 4P and supply is Q = –200 + 2P. Furthermore, suppose that the marginal external damage of this product is $8 per unit. How many more units of this product will the free market produce than is socially optimal? Calculate the deadweight loss associated with the externality.

To answer this question, first calculate what the free market would do by setting demand equal to supply: 1,200 – 4P = –200 + 2P, or 1,400 = 6P. P = 233.33, so QFree Market = 1,200 – 4(233.33) = 266.67. The socially optimal level occurs when the marginal external cost is included in the calculation. Suppose the $8 externality were added to the price each consumer had to pay. Then demand would be Q = 1,200 – 4(P + 8). Solving for P, 1,200 – 4(P + 8) = –200 + 2P, or P = 228. Solving for Q, 1,200 – 4(228 + 8) = 1,200 – 944. QSocial Opt = 256, 102/3 units less than provided by the free market. Deadweight loss is the area of a triangle of height 8 and distance 102/3: ½ (8 x 102/3) = 42.67. 14. The marginal damage averted from pollution cleanup is MD = 200 – 5Q. The marginal cost associated with pollution cleanup is MC = 10 + Q. a. What is the optimal level of pollution reduction?

Damage averted is the benefit, so solve by setting that equal to the marginal cost: 200 – 5Q = 10 + Q, or 312/3 . b. Show that this level of pollution reduction could be accomplished through taxation. What tax per unit would generate the optimal amount of pollution reduction?

This situation can be thought of as a market for pollution cleanup. Marginal damage averted is essentially willingness to pay for the cleanup, so it is the demand function; marginal cost of the cleanup is the supply function. Equilibrium in this market is at the quantity of 312/3 and a tax of 412/3. 15. Two firms are ordered by the federal government to reduce their pollution levels. Firm A’s marginal costs associated with pollution reduction are MC = 20 + 4Q. Firm B’s marginal costs associated with pollution reduction are MC = 10 + 8Q. The marginal benefit of pollution reduction is MB = 400 – 4Q. a. What is the socially optimal level of each firm’s pollution reduction?

For firm A, MC = MB when 20 + 4Q = 400 – 4Q, or when 380 = 8Q. Q A = 47.5. For firm B, it is 10 + 8Q = 400 – 4Q, or 390 = 12Q. QB = 32.5. Total reduction is 80 units.

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Jonathan Gruber / Finance and Public Policy

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b. Compare the social efficiency of three possible outcomes: (1) require both firms to reduce pollution by the same amount; (2) charge a common tax per unit of pollution; or (3) require both firms to reduce pollution by the same amount but allow pollution permits to be bought and sold.

1. The same level of pollution reduction could be achieved by requiring both firms to reduce pollution by 40 units. Firm A stops reducing pollution before it has exhausted all reduction steps for which the marginal cost is less than the marginal benefit, but firm B takes some pollution reduction steps for which the marginal cost exceeds marginal benefit. This is not socially efficient. 2. A common tax would yield the same result: a tax designed to be optimal for firm A would be too low to induce firm B to reduce to the efficient quantity, and a tax designed to be optimal for firm B would induce firm A to reduce by too much. 3. If the firms started at the pollution reduction levels suggested in part (1), a pollution permit market would allow firm A to reduce its pollution by 7.5 more units, and sell those permits to firm B, yielding the same result as in a. 16. One hundred commuters need to use a strip of highway to get to work. They all drive alone and prefer to drive in big cars—it gives them more prestige and makes them feel safer. Bigger cars cost more per mile to operate, since their gas mileage is lower. Worse yet, bigger cars cause greater permanent damage to roads. The weight of the car is w. Suppose that the benefits from driving are 4w, while the costs are (3/2)w2. The damage to roads is (1/3)w3. Assume that individuals have utility functions of the form U = x, where x are the net benefits from driving a car of a given size. Students who have taken calculus should be able to answer the following question if they understand marginal to mean a partial derivative. a. What car weight will be chosen by drivers?

If benefits are 4w, marginal benefits are 4. Similarly, if costs are (3/2)w2, marginal (private) cost is 3w. Private individuals who do not consider external costs will set MB = MC, or 4 = 3w, and choose a car that weighs 11/3. b. What is the optimal car weight? If this differs from a, why?

Social optimality requires MB = total marginal costs. In order to measure total marginal costs, you need to include the damage to the roads, (1/3)w3. The marginal damage is the first derivative of road damage with respect to weight, or w. Here the marginal external cost, the road damage, is w. Setting marginal benefits equal to total marginal costs gives the equation for optimality: 4 = 3w + w. Solving for w, when both private and external costs are included, yields w Social Optimal = 1. The optimal car weight, when all costs are included, is less than the optimal weight chosen by individuals when they ignore the external costs they impose. The reason is that internalizing the externality would make decision makers take into account the external cost. When they do, weight costs them more. c. Can you design a toll system that causes drivers to choose the optimal car weight? If so, then how would such a system work?

A toll just equal to the externality will internalize this externality. The marginal external cost was calculated to be w, the weight of the car, in 16b. Adding this cost to the private marginal cost of driving makes the total marginal cost of driving 4w. Individual

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Jonathan Gruber / Finance and Public Policy

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decision makers will reoptimize by setting private marginal benefit equal to the marginal cost they are now charged. Here it will be 4 = 4w. A private decision maker will choose w = 1, the socially optimal weight.

In-class Project An in-class demonstration of externalities and Coase’s solution is described in “The Paper River: A Demonstration of Externalities and Coase’s Theorem,” by Gail M. Hoyt, Patricia L. Ryan, and Robert G. Houston, Jr., Journal of Economic Education 30, no. 2 (Spring 1999), pp. 141–47. “The Paper River Revisited: A Common Property Externality Exercise,” by Thomas P. Andrews, Journal of Economic Education 33, no. 4 (Fall 2002), pp. 327—32, adds some nice refinements. In these experiments, “upstream producers” solve several multiplication problems in a short amount of time using small (approximately 1.5” x 2”) slips of paper and either a pen or pencil. I have used ten problems, each of which is a three-digit number multiplied by a two-digit number, with a time limit of three minutes. The upstream producers can buy either a pen or pencil to do their calculations. The pen costs the firm one point and the pencil costs the firm two points (the pen is the cheaper technology). Two points are awarded for each correct answer, and the cost of the pen or pencil is subtracted to yield the upstream firm’s total points for the round. The “downstream firms” then make paper airplanes, earning two points for each airplane successfully completed in three minutes. The catch is that the airplanes must be made of clean paper. If the upstream firm uses a pen, the paper is ruined and cannot be used for airplane production. If the upstream firm uses a pencil, the downstream firm can erase the marks and reuse the paper. If the upstream firm conserves on paper use, the downstream firm can make airplanes without having to erase. By participating in this exercise over three or four rounds, students are able to negotiate toward an efficient solution, where efficient is defined as maximizing points. This simulation can easily be completed in a one-hour class period. It helps to prepare several sets of ten math problems (each one a three-digit number multiplied by a two-digit number) ahead of time on transparencies, and to prepare a separate transparency for each set showing the answers. The original Paper River experiment involved several separate pairs, each consisting of one upstream and one downstream producer. Negotiations were limited to agreements between those firms. In the later version, the slips of paper were available to several producers of each type, demonstrating the difficulty of arriving at a Coasian solution when many parties are affected.

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Jonathan Gruber / Finance and Public Policy